Functions practice · Medium

$f\;:\left[ { - 4,0} \right] \to R$ is given by$f\left( x \right) = {e^x} + \sin x,$ its even extension to $\left[ { - 4,4} \right],$ is

If $\cos 2 x-a \sin x=2 a-7$, then range of $a$ is

Let $A \equiv\{1,2,3,4\}, B \equiv\{a, b, c\}$, then number of functions from $A \rightarrow B$, which are not onto i

Let $f(x)=\frac{\alpha x}{x+1}, x \neq 1$. Then for what value of $\alpha$, is $f(f(x))=x ?$

The domain of the function $f\left( {x\;} \right) = {\log _{2x - 1}}\left( {x - 1} \right)$ is

If $f: \mathbb{R} \rightarrow \mathbb{R} \& \quad g: \mathbb{R} \rightarrow \mathbb{R}$ be two given functions, then $2 \min \{f(x)-g(x), 0\}$ equals

Which of the following statement is true $(\mathrm{T})$ or false $(\mathrm{F})$ for the function $f: \mathrm{R} \rightarrow \mathrm{R}$ ?
(i) If $|f(x)-f(y)| \leq 30|x-y|, \forall x, y \in \mathrm{R}$, then $f$ is a continuous function on $\mathrm{R}$.
(ii) If $|f(x)-f(y)| \leq 30|x-y|, \forall x, y \in \mathrm{R}$, then $f$ is differentiable on $\mathrm{R}$.
(iii) If $|f(x)-f(y)| \leq 21|x-y|^2, \forall x, y \in \mathbb{R}$, then $f$ is differentiable on $\mathrm{R}$.
(iv) If $|f(x)-f(y)| \leq 21|x-y|^2, \forall x, y \in \mathrm{R}$, then $f$ is a constant function.

If $f(x)=\{x\}+\{x+1\}+\{x+2\} \ldots \ldots . . x+99\}$, then the value of $[f(\sqrt{2})]$ is, where $\{$.$\}$ denotes fractional part function & $[.]$ denotes the greatest integer function

If $f: R \rightarrow R$ is given by $f(x)=3 x-5$, then $f^{-1}(x)$ ?

Suppose that $g(x)=1+\sqrt{x}$ and $f(g(x))=3+2 \sqrt{x}+x$, then $f(x)$ is:

The range of the function $f\left( x \right) = \frac{1}{{2 - \cos 3\;x}},$ is

The range of the function $f(x)=\frac{x}{1+x^2}, x \in \mathbb{R}$ is

The domain of the function $f\left( x \right) = {\sin ^{ - 1}}\left( {{{\log }_3}\left( {x/3} \right)} \right)$ is

If $f(2 x+3 y, 2 x-7 y)=20 x$, then $f(x, y)$ equals

The value of the function $f\left( x \right) = 3\sin \left( {\sqrt {\frac{{{\pi ^2}}}{{16}} - {x^2}} } \right)$ lies in the interval

If $f(x)=x$ and $g(x)=|x|$, then $(f+g)(x)$ is equal to

$\left| {2x - 3} \right| < \left| {x + 5} \right|,$ then $x$ belongs to

Let $A=\{1,2,3,4\}$ and $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, a \times b$ is an even number $\}$, then the range of $R$ is

The range of the function $\left[4^x-2^{x+1}+1\right]$ is, where [.] represents the greatest integer function is

If $f\left( x \right)$ is defined on $\left[ {0,\;1} \right],$ then the domain of definition of $f\left( {\tan x} \right)$ is

A real valued function $f(x)$ satisfies the function equation $f(x-y)=f(x) f(y)-f(a-x) f(a+y)$ where $a$ is a given constant and $f(0)=1, f(2 a-x)$ is equal to

If $f(x)=\sin \log x$, then the value of $f(x y)+f\left(\frac{x}{y}\right)-2 f(x) \cdot \cos \log y$ is equal to

The domain of $F(x)=\frac{\log _2(x+3)}{x^2+3 x+2}$ is

The number of functions $f:\{1,2,3,4\} \rightarrow\{a \in: \mathbb{Z}|\alpha| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f(n+1)=1, \forall n \in\{1,2,3\}$ is

The range of the function ${ }^{7-x} P_{x-3}$ is

The least integer satisfying $49.4 - \left( {\frac{{27 - x}}{{10}}} \right) < 47.4 - \left( {\frac{{27 - 9x}}{{10}}} \right),$ is

If $f(x)=\frac{x-1}{x+1}$, then $f(f(a x))$ is equal to

The domain of the function $f(x)=\sin ^{-1}\left\{\log _2\left(\frac{1}{2} x^2\right)\right\}$ is

If $x,y\, \in \left\{ {1,2,3,4} \right\},$ then which ofthe following is/are function(s) in the given set?

The set of all values of ' $a$ 'for which the roots of the equation $(a+1) x^2-3 a x+4 a=0(a \neq-1)$ are real and greater than 1 is